theory, the resolvent set of a linear operator is a set of complex numbers for which the operator is in some sense "well-behaved". The resolvent set plays an...

theory Resolvent set in operator theory, the set of points where an operator is "well-behaved" Feller process § Resolvent in probability theory Resolvent (Galois...

In mathematics, the resolvent formalism is a technique for applying concepts from complex analysis to the study of the spectrum of operators on Banach...

denoted σ ( T ) {\displaystyle \sigma (T)} , and its complement, the resolvent set, is denoted ρ ( T ) = C ∖ σ ( T ) {\displaystyle \rho (T)=\mathbb {C}...

a bounded operator) is called the resolvent of T. The spectrum of T is therefore the complement of the resolvent set of T in the complex plane. Every eigenvalue...

differentiability can be made regarding the resolvent map. The resolvent set ρ(T) is actually an open set on which the resolvent map is analytic. This property will...

A is closed and D(A) is dense in X, every real λ > ω belongs to the resolvent set of A and for such λ and for all positive integers n, ‖ ( λ I − A ) −...

in terms of the resolvent operator of the generator: all λ with positive real part belong to the resolvent set of A and the resolvent operator is uniformly...

complement of the spectrum σ ( T ) {\displaystyle \sigma (T)} is known as resolvent set ρ ( T ) {\displaystyle \rho (T)} that is ρ ( T ) = C ∖ σ ( T ) {\displaystyle...

\setminus \sigma _{\mathrm {ess} ,1}(T)} that do not intersect with the resolvent set C ∖ σ ( T ) {\displaystyle \mathbb {C} \setminus \sigma (T)} . Each...